Accession Number:

AD0734169

Title:

A General Coupled Equation Approach for Solving the Biharmonic Boundary Value Problem,

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1971-11-01

Pagination or Media Count:

43.0

Abstract:

The biharmonic boundary value problem with Dirichlet boundary conditions is reduced to a coupled system of Poisson equations, which depend upon an arbitrary, positive coupling constant c. Since each of the Poisson equations is well-posed, the system may be solved by iteration. The author shows that the iterates may be represented as a linear combination of the eigenfunctions of the Dirichlet eigenvalue problem. Convergence of the iterative scheme occurs when O c 2 nu sub 1 where nu sub 1 is the smallest eigenvalue. By making use of an averaging scheme convergence may be produced for any positive c. With the proper choice of c, the rate of convergence may be increased. This coupled equation approach includes the finite difference approach as a special case. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE